Pulse width modulation is a technique that can be used for converting an analogue signal into a binary signal, by comparing the analogue signal with a periodic reference signal. Pulse width modulation is amongst others applied in class D amplifiers, which are often used in portable audiovisual appliances. Class D amplifiers are known for their relatively high power efficiency (energy losses are small), and relatively straightforward circuit design. This allows these amplification devices to be small, and makes them suitable for portable applications. Class D amplifiers are based on the principle that an incoming signal is compared with a periodic reference signal, such as a saw tooth or triangle wave. The amplification device comprises a switched amplifier which switches between a first and second voltage level dependent on whether the input voltage is higher or lower than the reference voltage than the voltage level of the reference signal.
The output of this switched amplifier is a high-frequency square wave with varying duty cycle. Prior to delivery to the load, this signal is first low-pass filtered by an LC low pass filter. The low pass filter prevents the fast on/off portion of the signal from reaching the load, while passing the average value without attenuation.
An amplifier constructed in this manner suffers from various imperfections. The first and second voltage levels are normally not stable and affect the overall gain dynamically. The switched output stage takes a finite time to switch from the first to second voltage levels and back, and the output state is uncertain during this interval. This manifests itself in harmonic distortion. Moreover, the LC output filter, as seen from the load, constitutes a parallel resonant circuit that has a high output impedance near the cut-off frequency of the filter. A low output impedance is desirable to make the frequency response of the amplifier independent of the load impedance.
These problems are most efficiently addressed using feedback error control. Apart from improving the reproduction quality of a class D amplifier, the feedback loop can also be advantageously used to cause a controlled oscillation, thus operating the amplifier in a self-oscillating mode, obviating the need to provide an external periodic reference signal, e.g. provided by a triangle wave oscillator.
High order control loops having at least one amplitude-limited state variable usually have several stable limit cycles (oscillation conditions) or “modes”. In linear (i.e. non-switching) systems, operation at any of these limit cycles is considered “instability”. In switching systems, intentional operation at one of these modes is called “self-oscillation”. In particular, self-oscillation can be applied in class D amplifiers as a means of significantly increasing their loop gain. Since in a self-oscillating class D amplifier it is no longer necessary to provide a periodic reference signal, the design may be simplified considerably.
Self-oscillating control loops only work well when operating in one particular mode, usually the highest frequency mode. Operation at another mode will either result in greatly deteriorated performance or may even be destructive. Self-oscillation is achieved by closing a suitable feedback loop around a zero crossing detector, i.e. around for example a class D amplifier.
The oscillation modes of a self-oscillating class D amplifier are usually calculated using the following two criteria, which are based on the Barkhausen criterium for sinewave oscillators:Arg(H(j·2·π·f))=0  (Eq. 1a)andd(Arg(H(j·2·π·f)))/df<0  (Eq. 1b)wherein H(s) is the loop function of the oscillation loop and f is the frequency. What this formula basically says is that the system can oscillate at a frequency where the phase shift of the loop is 2π (or 0) radians. These criteria settle at several frequencies, also known as modes of operation.
High order loop control entails several problems. Firstly, when an amplifier containing one or multiple integrators is overmodulated (clipped), the error between input and output is large. The integrators will keep integrating this error for the entire time the output spends in clip. Once the input signal returns to the normal range, the output remains clipped until the integrated error becomes zero again. Recovery from clipping therefore happens rather slowly, causing a distortion in the output signal that lasts until the circuit is fully recovered.
Secondly, in view of the Barkhausen criterium a loop may be potentially capable of oscillating at unwanted frequencies. This is will almost certainly happen when the loop is optimised for maximum loop gain. A designer then counts on gain margin (the surplus gain over unity in a loop magnitude response being greater than unity when the phase difference is at (multiples of) 2π), not phase margin, to prevent the circuit from oscillating at unwanted frequencies. However, when a high order control loop is clipped, gain margin effectively collapses giving the circuit the opportunity to oscillate at a lower (unstable) frequency mode.
Thirdly, a control loop has only enough degrees of freedom for a designer to fix either the closed loop response (out of which the open loop response follows) or the open loop response (out of which the closed loop response follows) but not both. The normal procedure in class D amplifiers is to design for loop gain and to correct the frequency response externally.